Problem: Jessica is 4 times as old as Kevin. Fifteen years ago, Jessica was 9 times as old as Kevin. How old is Jessica now?
Answer: We can use the given information to write down two equations that describe the ages of Jessica and Kevin. Let Jessica's current age be $j$ and Kevin's current age be $k$ The information in the first sentence can be expressed in the following equation: $j = 4k$ Fifteen years ago, Jessica was $j - 15$ years old, and Kevin was $k - 15$ years old. The information in the second sentence can be expressed in the following equation: $j - 15 = 9(k - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $j$ , it might be easiest to solve our first equation for $k$ and substitute it into our second equation. Solving our first equation for $k$ , we get: $k = j / 4$ . Substituting this into our second equation, we get: $j - 15 = 9($ $(j / 4)$ $- 15)$ which combines the information about $j$ from both of our original equations. Simplifying the right side of this equation, we get: $j - 15 = \dfrac{9}{4} j - 135$ Solving for $j$ , we get: $\dfrac{5}{4} j = 120$ $j = \dfrac{4}{5} \cdot 120 = 96$.